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Stochastic arbitrage with market index options

Author

Listed:
  • Brendan K. Beare
  • Juwon Seo
  • Zhongxi Zheng

Abstract

Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset, generates a payoff which stochastically dominates the payoff from the direct investment in the underlying asset. We provide linear and mixed-integer linear programs for computing the stochastic arbitrage opportunity providing the maximum option premium to an investor. We apply our programs to 18 years of data on monthly put and call options on the Standard & Poors 500 index, confining attention to options with moderate moneyness, and using two specifications of the underlying asset return distribution, one symmetric and one skewed. The pricing of market index options with moderate moneyness appears to be broadly consistent with our skewed specification of market returns.

Suggested Citation

  • Brendan K. Beare & Juwon Seo & Zhongxi Zheng, 2022. "Stochastic arbitrage with market index options," Papers 2207.00949, arXiv.org, revised May 2024.
  • Handle: RePEc:arx:papers:2207.00949
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    References listed on IDEAS

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    1. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
    2. Brendan K. Beare, 2023. "Optimal measure preserving derivatives revisited," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 370-388, April.
    3. Ranadeb Chaudhuri & Mark Schroder, 2015. "Monotonicity of the Stochastic Discount Factor and Expected Option Returns," The Review of Financial Studies, Society for Financial Studies, vol. 28(5), pages 1462-1505.
    4. Dmitriy Muravyev & Neil D Pearson & Stijn Van Nieuwerburgh, 2020. "Options Trading Costs Are Lower than You Think," The Review of Financial Studies, Society for Financial Studies, vol. 33(11), pages 4973-5014.
    5. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    6. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    7. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-393, July.
    8. Peter Christoffersen & Steven Heston & Kris Jacobs, 2013. "Capturing Option Anomalies with a Variance-Dependent Pricing Kernel," The Review of Financial Studies, Society for Financial Studies, vol. 26(8), pages 1963-2006.
    9. George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2020. "Mispriced index option portfolios," Financial Management, Financial Management Association International, vol. 49(2), pages 297-330, June.
    10. Brendan K. Beare & Lawrence D. W. Schmidt, 2016. "An Empirical Test of Pricing Kernel Monotonicity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 338-356, March.
    11. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    12. George M. Constantinides & Michal Czerwonko & Jens Carsten Jackwerth & Stylianos Perrakis, 2011. "Are Options on Index Futures Profitable for Risk‐Averse Investors? Empirical Evidence," Journal of Finance, American Finance Association, vol. 66(4), pages 1407-1437, August.
    13. repec:bla:jfinan:v:58:y:2003:i:5:p:1905-1932 is not listed on IDEAS
    14. Beare, Brendan K., 2011. "Measure preserving derivatives and the pricing kernel puzzle," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 689-697.
    15. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    16. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    17. Russell Davidson, 2009. "Testing for Restricted Stochastic Dominance: Some Further Results," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 1(1), pages 34-59, September.
    18. Fousseni Chabi-Yo & René Garcia & Eric Renault, 2008. "State Dependence Can Explain the Risk Aversion Puzzle," The Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 973-1011, April.
    19. Levy, Haim, 1985. "Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach," Journal of Finance, American Finance Association, vol. 40(4), pages 1197-1217, September.
    20. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle in forward looking data," Review of Derivatives Research, Springer, vol. 21(3), pages 253-276, October.
    21. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    22. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    23. Brendan K. Beare & Asad Dossani, 2018. "Option augmented density forecasts of market returns with monotone pricing kernel," Quantitative Finance, Taylor & Francis Journals, vol. 18(4), pages 623-635, April.
    24. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    25. Stylianos Perrakis, 2022. "From innovation to obfuscation: continuous time finance fifty years later," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(3), pages 369-401, September.
    26. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    27. Perrakis, Stylianos & Ryan, Peter J, 1984. "Option Pricing Bounds in Discrete Time," Journal of Finance, American Finance Association, vol. 39(2), pages 519-525, June.
    28. Matthew Linn & Sophie Shive & Tyler Shumway, 2018. "Pricing Kernel Monotonicity and Conditional Information," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 493-531.
    29. Thierry Post & Iňaki Rodríguez Longarela, 2021. "Risk Arbitrage Opportunities for Stock Index Options," Operations Research, INFORMS, vol. 69(1), pages 100-113, January.
    30. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    31. Ritchken, Peter H, 1985. "On Option Pricing Bounds," Journal of Finance, American Finance Association, vol. 40(4), pages 1219-1233, September.
    32. Stylianos Perrakis, 2019. "Stochastic Dominance Option Pricing," Springer Books, Springer, number 978-3-030-11590-6, December.
    33. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
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